Details

Time bar (total: 30.2s)

sample75.0ms

Algorithm
intervals
Results
24.0ms292×body80valid
11.0ms33×body640valid
10.0ms20×body1280valid
8.0ms17×body320valid
2.0ms15×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
012684
126684
267684
3241684
41263684
done5000684

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
4.8b
(* (* x (pow sin 2.0)) x)
7.8b
(* x (pow sin 2.0))
18.4b
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
122×add-exp-log
82×prod-exp
34×add-cbrt-cube
18×pow-to-exp pow-exp
17×add-sqr-sqrt
16×div-exp cbrt-unprod
12×*-un-lft-identity add-cube-cbrt
11×associate-*r* associate-*l*
7×unpow-prod-down
6×pow1
4×expm1-log1p-u cbrt-undiv log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 123
Calls
4 calls:
63.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
30.0ms
(* (* x (pow sin 2.0)) x)
16.0ms
(* x (pow sin 2.0))
62.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

series1.1s

Counts
4 → 12
Calls
4 calls:
408.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x)))
167.0ms
(* (* x (pow sin 2.0)) x)
185.0ms
(* x (pow sin 2.0))
324.0ms
(* (pow cos 2.0) (* (* x (pow sin 2.0)) x))

simplify1.9s

Counts
135 → 135
Iterations

Useful iterations: 2 (604.0ms)

IterNodesCost
017476008
144867690
2240266320
done500166320

prune837.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 15.6b

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
4.8b
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
18.4b
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

rewrite605.0ms

Algorithm
rewrite-expression-head
Rules
416×add-exp-log
343×prod-exp
84×pow-to-exp pow-exp
52×add-cbrt-cube
43×div-exp
29×cbrt-unprod
11×add-sqr-sqrt *-un-lft-identity associate-*r* add-cube-cbrt
9×associate-*l*
6×pow1 unpow-prod-down
5×cbrt-undiv
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 194
Calls
4 calls:
32.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
236.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
84.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
238.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

series960.0ms

Counts
4 → 12
Calls
4 calls:
165.0ms
(* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2)))
364.0ms
(/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)))
150.0ms
(* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x)
280.0ms
(* (pow cos 2.0) (* (* (* x (pow sin (/ 2.0 2))) (pow sin (/ 2.0 2))) x))

simplify3.1s

Counts
206 → 206
Iterations

Useful iterations: done (3.0s)

IterNodesCost
0206143206
1588106350
23801102488
done500299870

prune801.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.6b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))))
4.1b
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2))))
10.5b
(* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
1691×add-exp-log
1549×prod-exp
399×pow-to-exp pow-exp
157×div-exp
92×add-cbrt-cube
59×cbrt-unprod
12×add-sqr-sqrt
11×pow1
10×*-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
7×cbrt-undiv unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l* unswap-sqr sqr-pow
1×pow2 clear-num associate-/r* frac-2neg pow-plus swap-sqr pow-prod-down pow-sqr pow-prod-up div-inv
Counts
4 → 478
Calls
4 calls:
36.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
355.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))))
380.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2))))
153.0ms
(* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
278.0ms
(* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2))))
488.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))))
409.0ms
(* (pow cos (/ 2.0 2)) (* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2))))
468.0ms
(* (* (* x (pow sin (/ 2.0 2))) (* x (pow sin (/ 2.0 2)))) (pow cos (/ 2.0 2)))

simplify3.6s

Counts
490 → 490
Iterations

Useful iterations: done (3.5s)

IterNodesCost
0279418867
1871289669
24303267945
done5000254994

prune989.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))
0.7b
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))))
3.3b
(* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))
4.1b
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))))

rewrite754.0ms

Algorithm
rewrite-expression-head
Rules
1711×add-exp-log
1564×prod-exp
400×pow-to-exp pow-exp
160×div-exp
97×add-cbrt-cube
62×cbrt-unprod
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×associate-*r* associate-*l*
8×cbrt-undiv
6×pow1 unpow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×times-frac *-commutative associate-/l*
2×sqr-pow
1×clear-num associate-/r* frac-2neg pow-prod-down div-inv
Counts
4 → 474
Calls
4 calls:
111.0ms
(* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))
257.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))))
24.0ms
(* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))
285.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))))

series2.0s

Counts
4 → 12
Calls
4 calls:
434.0ms
(* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))
442.0ms
(/ (cos (* 2.0 x)) (* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2))))))
283.0ms
(* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))
795.0ms
(* (pow cos (/ 2.0 2)) (* (* x (pow sin (/ 2.0 2))) (* (* x (pow sin (/ 2.0 2))) (pow cos (/ 2.0 2)))))

simplify4.4s

Counts
486 → 486
Iterations

Useful iterations: done (4.3s)

IterNodesCost
0280429083
1898282031
24966258730
done5000253720

prune713.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 1.2b

regimes740.0ms

Accuracy

0% (0.7b remaining)

Error of 2.7b against oracle of 2.0b and baseline of 2.7b

bsearch0.0ms

simplify9.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
015765
118725
219725
done19725

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.2s9056×body80valid
1.0s1005×body640valid
539.0ms780×body1280valid
297.0ms537×body320valid
76.0ms330×body160valid